There is no way to read a Processor Serial Number in software. You can extract information about the processor using the CPUID instruction; there are lots of programs around that can do that.
For starters, download and run the Intel Processor Identification Utility. It is available here: https://downloadcenter.intel.com/download/28539/Intel-Processor-Identification-Utility-Windows-Versi....
You could also download and run the Intel Processor Diagnostic Tool. It is available here: https://downloadcenter.intel.com/download/19792/Intel-Processor-Diagnostic-Tool?product=5982
If these don't get you what you need, then you will have to pull the heatsink off.